That would require plugins which are being phased out and for good reason.
Namely, because they allow something like Adobe Flash Player - which doesn't come close to supporting all the platforms the Web runs on - to become a defacto standard. Thus restricting a large portion of the Web to just a few platforms Adobe wants to support.
That's one way of looking at it. OTOH, not allowing plugins arbitrarily restricts web users to the lowest common denominator of technologies that are supported by browser vendors. Why should I care to have my technology choices dictated by browser vendors any more than I care to have them dictated by Adobe?
That said, nothing about what I'm proposing specifically requires plugins. All it would require would be for the browser vendors to work together (cough, cough, I know, coughcough) to implement a standard mechanism for doing this. Actually, it might not even take that. Browsers already have a way to setup handlers for unsupported content types and what-not, so it might be possible to build what I'm thinking about largely on top of that. Of course it would mean that if you wanted to run an "application" UI you'd have to have a suitable platform (an X server, or something like an X server) running along-side your browser. So you maybe wouldn't be able to run OpenOffice on your smart-phone. OK, personally, I can live with that. Not all devices are equivalent and there's no reason to expect every thing to work one every device.
Namely, because they allow something like Adobe Flash Player - which doesn't come close to supporting all the platforms the Web runs on - to become a defacto standard. Thus restricting a large portion of the Web to just a few platforms Adobe wants to support.